About random number generator

KVS has the two types of the random number generator:

 

In this page, we explain the member function of the random class, and then, Let’s calculate the circumference ratio by using the Monte Carlo method. Moreover, we obtain the average and variance.

 

Member functions

Constructor

There are two types of constructor.

If you set the seed, the random number sequence is fixed.

// Default constructor

kvs::MersenneTwister uniRand;      // uniform random

kvs::BoxMuller normRand;      // normal random

// Set to a seed for the random number generator

kvs::MersenneTwister uniRand2( 261422 );      // uniform random

kvs::BoxMuller normRand2( 261422 );      // normal random

Generation of random number

perator (): generation of random number

KVS sets as default random number:

std::cout << "[0, 1] : uniform random " << uniRand() << std::endl;

std::cout << "N(0, 1) : normal random " << normRand() << std::endl;

 

std::cout << "[0, 1] : uniform random " << uniRand2() << std::endl;

std::cout << "N(0, 1) : normal random " << normRand2() << std::endl;

Change the distribution

Uniformly distributed in [0, n] :

　　rand( const double n )

ormal distribution as N(mu, sigma2):

　　rand( const double mu, const double sigma2 )

　　where mu; average，sigma2 ：variance.

// Change the distribution

std::cout << "[0, 100] : uniform random " << uniRand.rand( 100 ) << std::endl;

std::cout << "N(2, 10) : normal random " << normRand.rand(2, 10) << std::endl;

 

Example: Calculate π by using the Monte Carlo method

 

If the circle of radius r is inscribed inside the square with side length 2r, then the area of the circle will be π*r^2 and the area of the square will be (2r)^2. The ratio of the area of the circle to the area of the square will be π/4.

In this example, r=1, and, the random number is generated in[0, 1]×[0, 1], and then, you count the number of pints inside the circle x2 + y2 < 1 .

 

1. Make a working directory

First, please create a working directory where you will run the program (e.g., CreateRandom).

# mkdir  CreateRandom

# cd CreateRandom

 

2.　Programming

In order to generate the uniform random, you create an instance of kvs::MersenneTwister.

In this example, the number of trials is fixed as 1000.

For example:

int main( void )

{

    kvs::MersenneTwister uniRand;        // uniform random

 

    // Number of trials

    const int trialNum = 1000;

 

    return ( 0 );

}

 

3.　Initializing

The variable for counting the number of point inside the circle set to zero. In addition, the variables for calculating the average and the variance set to zero.

// For counting the number of point

int num = 0;

// Average and variance

double uniAve = 0.0, uniDp = 0.0;

 

4. Counting

you count the number of pints inside the circle x2 + y2 < 1 .

for( int i=0; i<trialNum; i++ ) {

    // Generate random number

    double x = uniRand();

    double y = uniRand();

    // Count the number of point inside the circle

    if( ( x*x + y*y ) < 1.0 )

        num++;

 

    // Calculate the sum and square sum

    uniAve += x;

    uniDp += ( x * x );

}

 

5. Calculate π

In order to obtain pi, you calculate the ratio of the number the number of point inside the circle to all number of generated points.

// calculate pi

double pi = (double)num/(double)trialNum * 4.0;

std::cout << num << " " << trialNum << std::endl;

std::cout << "pi: " << pi << std::endl;

 

// average and variance

uniAve /= (double)trialNum;

uniDp = uniDp/(double)trialNum - uniAve*uniAve;

std::cout << "-- uniform random number-- " << std::endl;;

std::cout << "Average : " << uniAve << " Variance : " << uniDp << std::endl;

 

6.　Sample program

Sample program: CreateRandom.tgz

 

7.　Compile and execute

Let's try to compile and execute above program.

When compiling a KVS program, it is easy to use the automatic Makefile-generation tool kvsmake supplied by KVS.

# kvsmake -G　　　　　　　　　　<-- Generate Makefile

# kvsmake　　　　　　　　　　　　<-- Compile

And then,

# ./CreateRandom　

　===== execution result =====

[0, 1] : Uniform random 0.878668

N(0, 1) : normal random 0.0767265

[0, 1] : Uniform random 0.606438

N(0, 1) : normal random -0.447015

[0, 100] : Uniform random number 76.839

N(2, 10) : normal random 12.1152

pi : 3.136

-- Uniform random Number --

Average : 0.503782 Variance : 0.0857954

 

 

 

 

Last Updated at Nov. 1, 2015　

 

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